The Catholic Church can traditionally canonize at a local level but only through the permission of a local bishop. More canonizations nowadays are done directly through Rome which requires more than popular acclamation though popular veneration is a key component to getting considered for sainthood.

The Catholic Church's beatification and canonization is pretty official and handled/monopolize by the church. Also you just become this demigod thing.

The Chinese case is very informal and just relies on sheer popular acclaim for a dead person. Plus you become a fullblown god.

I think it's like Marvel and DC, either or, you don't get to cross over

Sainthood is a process. You do need a lot of people to know your name and accomplishments to achieve beatification (recognition) but you need several miracles attributed to you in order to be canonized. This process is controlled by the Church. There are numerous small folk saints people pray to but aren’t recognized by the church. Some Mexicans might pray to Pancho Villa or Jesus Malvedre, some southern Americans might pray to Marie Laveau, some Brits might pray to Catherine of Aragon, some Latin American criminals might pray to the Santa Muerte but none of these are prayed to outside of certain regions, lack miracles, and aren’t recognized by the Church or the larger community. Btw La Santa Muerte isn’t even Catholic and those who do worship it are Satanists and cartel members.

Canonization doesn't declare people to be gods.